Question: $J$ $K$ $L$ If: $ KL = 8x + 2$, $ JK = 6x + 7$, and $ JL = 107$, Find $KL$.
Explanation: From the diagram, we can see that the total length of ${JL}$ is the sum of ${JK}$ and ${KL}$ $ {JK} + {KL} = {JL}$ Substitute in the expressions that were given for each length: $ {6x + 7} + {8x + 2} = {107}$ Combine like terms: $ 14x + 9 = {107}$ Subtract $9$ from both sides: $ 14x = 98$ Divide both sides by $14$ to find $x$ $ x = 7$ Substitute $7$ for $x$ in the expression that was given for $KL$ $ KL = 8({7}) + 2$ Simplify: $ {KL = 56 + 2}$ Simplify to find ${KL}$ : $ {KL = 58}$